Abstract. This article is concerned with the asymptotic accuracy of the Computational Singular Perturbation (CSP) method developed by Lam and Goussis to reduce the dimensionality of a system of chemical kinetics equations. The method exploits the presence of disparate time scales to model the dynamics by an evolution equation on a lower-dimensional slow manifold. In this article it is shown tha...

A key challenge of single-cell RNASeq (scRNASeq) is the many genes with zero reads in some cells, but high expression in others. Modelling zeros using the Michaelis-Menten equation provides a superior fit to existing scRNASeq datasets compared to other approaches and enables fast and accurate identification of features corresponding to differentially expressed genes without prior identification...

Inulosucrases catalyze transfer of a fructose moiety from sucrose to a water molecule (hydrolysis) or to an acceptor molecule (transferase), yielding inulin. Bacterial inulin production is rare and a biochemical analysis of inulosucrase enzymes has not been reported. Here we report biochemical characteristics of a purified recombinant inulosucrase enzyme from Lactobacillus reuteri. It displayed...

It is not always clear that some equations affected by complicated factors can, actually, be interpreted as a ratio of two polynomials of first degree and so that they can be, in general, represented by rectangular hyperbolas. In this paper we present an easy procedure to rearrange those equations into Michaelis-Menten-type equations and so to make the aspects of these rectangular hyperbolas mo...

Single-cell RNA sequencing is able to quantify the whole transcriptome from the small amount of RNA present in individual cells. However, a consequence of reverse-transcribing and amplifying small quantities of RNA is a large number of dropouts, genes with zero expression in particular cells. The frequency of dropout events is strongly non-linearly related to the measured expression levels of t...

Brain slice glucose utilization (SGU) can be measured by methods analogous to those used for in vivo cerebral glucose utilization. In order to make this technique more accessible and applicable to a broad range of experimental conditions, we have derived a simplified operational rate equation and generated the table of apparent rate coefficients necessary to apply the equation under different e...

Enzyme hydrolysis kinetic model of inulin by inulinase from Kluyveromyces lactis was established. The corresponding Michaelis-Menten equation model constants were found to be related to temperature through the Arrhenius model. The kinetic model was validated by experimental data and also be utilized to predict the hydrolysis reaction rates of the inulin for substrate concentrations ranging betw...

For enzymatic progress curves conforming to the Michaelis–Menten mechanism (E + S ES → E + P) under the experimental conditions where the substrate concentration is at least several times smaller than the Michaelis constant, the minimal fitting model cast as a system of numerically integrated differential equations is the simple ‘hit-and-run’ mechanism, E + S → E + P. The best-fit value of sing...

The statistical implications of the direct linear plot for enzyme kinetic data, described in the preceding paper (Eisenthal & Cornish-Bowden, 1974), are discussed for the case of the Michaelis-Menten equation. The plot is shown to lead directly to non-parametric confidence limits for the kinetic parameters, V and K(m), which depend on far less sweeping assumptions about the nature of experiment...

The site specific endonuclease Bam HI which is composed of subunits of a molecular weight of 22 000 [1] can aggregate to complexes of a molecular weight of 360 000. It is an acidic protein with an isoelectric point at pH 5.3. Optimal activity is reached at 13 mM MgCl2. A very simple method is presented to determine kinetic constants of restriction enzymes directly from agarose gel photographs w...